{"id":"https://openalex.org/W4280556842","doi":"https://doi.org/10.1007/s10898-022-01161-z","title":"On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints","display_name":"On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints","publication_year":2022,"publication_date":"2022-05-13","ids":{"openalex":"https://openalex.org/W4280556842","doi":"https://doi.org/10.1007/s10898-022-01161-z"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-022-01161-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01161-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01161-z.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01161-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077659287","display_name":"Holger Heitsch","orcid":"https://orcid.org/0000-0002-2692-4602"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Heitsch","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111442239","display_name":"Ren\u00e9 Henrion","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Henrion","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006634255","display_name":"Thomas Kleinert","orcid":"https://orcid.org/0000-0001-7082-7466"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Kleinert","raw_affiliation_strings":["Energie Campus N\u00fcrnberg, F\u00fcrther Str. 250, 90429, Nuremberg, Germany","Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Discrete Optimization, Cauerstr. 11, 91058, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Energie Campus N\u00fcrnberg, F\u00fcrther Str. 250, 90429, Nuremberg, Germany","institution_ids":[]},{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Discrete Optimization, Cauerstr. 11, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002857019","display_name":"Martin Schmidt","orcid":"https://orcid.org/0000-0001-6208-5677"},"institutions":[{"id":"https://openalex.org/I89864525","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05","country_code":"DE","type":"education","lineage":["https://openalex.org/I89864525"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Schmidt","raw_affiliation_strings":["Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6208-5677","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany","institution_ids":["https://openalex.org/I89864525"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002857019"],"corresponding_institution_ids":["https://openalex.org/I89864525"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":{"value":2780,"currency":"USD","value_usd":2780},"fwci":0.6053,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60069916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"84","issue":"3","first_page":"651","last_page":"685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10969","display_name":"Water resources management and optimization","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10969","display_name":"Water resources management and optimization","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10471","display_name":"Climate Change Policy and Economics","score":0.96670001745224,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.8557996153831482},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7382122874259949},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.695838212966919},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.6596190929412842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5744460821151733},{"id":"https://openalex.org/keywords/black-box","display_name":"Black box","score":0.5661930441856384},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4790440797805786},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4506787955760956},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4505763351917267},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4322758913040161},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4130287766456604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3028745651245117},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08490714430809021},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.07155242562294006}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.8557996153831482},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7382122874259949},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.695838212966919},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.6596190929412842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5744460821151733},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.5661930441856384},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4790440797805786},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4506787955760956},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4505763351917267},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4322758913040161},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4130287766456604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3028745651245117},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08490714430809021},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.07155242562294006},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-022-01161-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01161-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01161-z.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:doi:10.20347/wias.preprint.2828","is_oa":false,"landing_page_url":"http://localhost:8291/receive/wias_mods_00006827","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:RePEc:spr:jglopt:v:84:y:2022:i:3:d:10.1007_s10898-022-01161-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-022-01161-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:econstor.eu:10419/307498","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/307498","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10898-022-01161-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-022-01161-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-022-01161-z.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G5928542188","display_name":null,"funder_award_id":"projects A05","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6692072944","display_name":null,"funder_award_id":"Transregio 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7491996025","display_name":null,"funder_award_id":"TRR 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323744","display_name":"\u00c9lectricit\u00e9 de France","ror":"https://ror.org/03wb8xz10"},{"id":"https://openalex.org/F4320324478","display_name":"Fondation Math\u00e9matique Jacques Hadamard","ror":"https://ror.org/0153me927"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280556842.pdf","grobid_xml":"https://content.openalex.org/works/W4280556842.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1499399028","https://openalex.org/W1588628884","https://openalex.org/W1891298814","https://openalex.org/W1967737508","https://openalex.org/W1970933528","https://openalex.org/W1971796369","https://openalex.org/W2005629858","https://openalex.org/W2048068372","https://openalex.org/W2053391173","https://openalex.org/W2056831000","https://openalex.org/W2057338659","https://openalex.org/W2060743072","https://openalex.org/W2061614157","https://openalex.org/W2069808690","https://openalex.org/W2071334094","https://openalex.org/W2074376561","https://openalex.org/W2079104779","https://openalex.org/W2080474145","https://openalex.org/W2082477992","https://openalex.org/W2105935934","https://openalex.org/W2138865117","https://openalex.org/W2162708400","https://openalex.org/W2164945937","https://openalex.org/W2165383819","https://openalex.org/W2403192619","https://openalex.org/W2479349391","https://openalex.org/W2499145065","https://openalex.org/W2569380384","https://openalex.org/W2622645533","https://openalex.org/W2745660793","https://openalex.org/W2754261171","https://openalex.org/W2756033884","https://openalex.org/W2785764032","https://openalex.org/W2798344481","https://openalex.org/W2891879843","https://openalex.org/W2902579153","https://openalex.org/W2920846954","https://openalex.org/W2951762099","https://openalex.org/W2953647592","https://openalex.org/W2963920200","https://openalex.org/W3004643923","https://openalex.org/W3038643818","https://openalex.org/W3106639163","https://openalex.org/W3107332689","https://openalex.org/W3107565123","https://openalex.org/W3157498319","https://openalex.org/W3174839186","https://openalex.org/W3194404705","https://openalex.org/W3208100382","https://openalex.org/W4251616545","https://openalex.org/W4252291168","https://openalex.org/W4389880031"],"related_works":["https://openalex.org/W2363414825","https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W3126901467","https://openalex.org/W2161149697","https://openalex.org/W3090200643","https://openalex.org/W2340378315","https://openalex.org/W255338418","https://openalex.org/W2013038594","https://openalex.org/W1604175135"],"abstract_inverted_index":{"Abstract":[0],"Bilevel":[1],"optimization":[2],"is":[3,96],"an":[4],"increasingly":[5],"important":[6],"tool":[7],"to":[8,24,71,88,119,136,144,157],"model":[9,74,89],"hierarchical":[10],"decision":[11],"making.":[12],"However,":[13],"the":[14,36,51,76,93,105,111,123,127,141,159,165],"ability":[15],"of":[16,39,42,75,126,164,169],"modeling":[17],"such":[18],"settings":[19],"makes":[20],"bilevel":[21,73,128],"problems":[22,43],"hard":[23],"solve":[25,140],"in":[26,50,80,99,162],"theory":[27],"and":[28],"practice.":[29],"In":[30,148],"this":[31,40,55,69,102],"paper,":[32],"we":[33,57,82,114,133,139,153],"add":[34],"on":[35,122],"general":[37],"difficulty":[38],"class":[41],"by":[44],"further":[45,116],"incorporating":[46],"convex":[47],"black-box":[48,106],"constraints":[49],"lower":[52],"level.":[53],"For":[54,110],"setup,":[56],"develop":[58],"a":[59,72,84],"cutting-plane":[60],"algorithm":[61],"that":[62,138],"computes":[63],"approximate":[64,145],"bilevel-feasible":[65],"points.":[66],"We":[67],"apply":[68],"method":[70],"European":[77],"gas":[78],"market":[79],"which":[81],"use":[83,115],"joint":[85],"chance":[86,94],"constraint":[87,95],"uncertain":[90,170],"loads.":[91],"Since":[92],"not":[97],"available":[98],"closed":[100],"form,":[101],"fits":[103],"into":[104],"setting":[107],"studied":[108],"before.":[109],"applied":[112],"model,":[113],"problem-specific":[117],"insights":[118],"derive":[120],"bounds":[121],"objective":[124],"value":[125],"problem.":[129],"By":[130],"doing":[131],"so,":[132],"are":[134,154],"able":[135,156],"show":[137],"application":[142],"problem":[143],"global":[146],"optimality.":[147],"our":[149],"numerical":[150],"case":[151],"study":[152],"thus":[155],"evaluate":[158],"welfare":[160],"sensitivity":[161],"dependence":[163],"achieved":[166],"safety":[167],"level":[168],"load":[171],"coverage.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
